Simulation-Based Inference of Ginzburg--Landau Parameters in Type--1.5 Superconductors

Inferring microscopic couplings in multi-component superconductors directly from vortex configurations is a challenging inverse problem. In Type-1.5 systems, Time-Dependent Ginzburg-Landau (TDGL) dynamics generate complex, glassy vortex patterns with high metastability. We explicitly quantify this intractability by analyzing the Hessian spectrum of the energy landscape, revealing a proliferation of soft modes that hinders traditional sampling. We address this challenge by combining a differentiable TDGL solver with Simulation-Based Inference (SBI). Our approach treats the solver as a stochastic forward model mapping physical parameters ({\theta} = ({\eta}, B, {\nu})) to vortex density fields. Using Neural Ratio Estimation (NRE), we train a classifier to approximate the likelihood-to-evidence ratio and perform Bayesian inference for the interband Josephson coupling from vortex density fields. On synthetic data, the proposed method reliably recovers the coupling with calibrated uncertainty.